Is "fake teeth" correct?
Solution 1:
Maybe your English tutor wants you to say "false teeth" instead. Google count is 85K for "fake teeth" and 442K for "false teeth".
Note that in the Wikipedia, both "false teeth" and "fake teeth" redirect to the page on dentures. However, in general, while "false teeth" is used as a synonym for dentures, "fake teeth" is more for things like vampire teeth that people wear in Halloween for fun.